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Abstract

We develop a method for synthesis of a desired intensity profile at the output of a multimode fiber (MMF) with random mode coupling by controlling the input field distribution using a spatial light modulator (SLM) whose complex reflectance is piecewise constant over a set of disjoint blocks. Depending on the application, the desired intensity profile may be known or unknown a priori. We pose the problem as optimization of an objective function quantifying, and derive a theoretical lower bound on the achievable objective function. We present an adaptive sequential coordinate ascent (SCA) algorithm for controlling the SLM, which does not require characterizing the full transfer characteristic of the MMF, and which converges to near the lower bound after one pass over the SLM blocks. This algorithm is faster than optimizations based on genetic algorithms or random assignment of SLM phases. We present simulated and experimental results applying the algorithm to forming spots of light at a MMF output, and describe how the algorithm can be applied to imaging.

Figures (9)

System for synthesis of a known intensity pattern. Light from a laser illuminates an SLM, and light reflected from the SLM is focused into an MMF. At the MMF output, the intensity distribution is measured using a microscope and camera. The goal is to find an SLM pattern such that the output intensity distribution approximates a desired distribution. The inset shows the two regions R1 and R2 at the MMF output used in defining the objective function for synthesizing a known intensity profile.

Characteristics of the spots formed using CPSCA and APSCA in known locations at different distances from the center of the fiber, in simulation and experiment: (a) longitudinal spot size, (b) transverse spot size, (c) centroid location, (d) peak sidelobe ratio and (e) integrated sidelobe ratio. Note that CPSCA and APSCA yield higher peak and integrated sidelobe ratios than a backpropagated delta function sampled at the same resolution.

Normalized objective function convergence curve for a spot in a known location 5 µm from the center of the fiber, for simulated (solid) and experimental (dashed) CPSCA. In both cases, after one pass over the SLM, the objective function converges to a value close to the theoretical lower bound.

Experimental setup for forming spots in known locations and for imaging. Light from a 1550-nm laser is directed onto the SLM. Light reflected from the SLM is focused into the MMF. A camera measures the intensity profile at the MMF output and sends the data to a PC that controls the SLM phases. The inset shows an imaging mode of operation, where a test object is placed in front of the fiber. Previously saved patterns are loaded on the SLM to generate spots of light at different locations on the fiber output. The spots sample the test object and the reflected intensity is measured by the power meter and used to reconstruct the image.

Simulated intensity distributions formed in unknown locations at the output of a 50-μm parabolic-index MMF. Fluorophore distributions having 4-μm FWHM are centered: (a) at center of core, (b) 10 µm away from center of core and (c) 20 µm away from center of core. No a priori knowledge of the fluorophore location is assumed. Adaptive CPSCA is used on a phase-only SLM with 16 × 16 blocks to maximize the total back-reflected fluorescent light intensity. White circles show the fiber core boundary.

Normalized objective function convergence curve for targeted light delivery to a fluorophore distribution having 4-μm FWHM and centered 10 µm away from center of core, for adaptation by CPSCA. After one pass over the SLM, the objective function converges to a value close to the theoretical lower bound.

Simulated imaging of an infinite checkerboard using spots formed by (a-c) backpropagated delta functions sampled by an infinite-resolution amplitude-and-phase SLM (a-c) and (d-f) by adaptive CPSCA using a 16 × 16-block SLM. The square size is (a),(d) 3.5 µm, (b),(e) 4.5 µm, and (c),(f) 5.5 µm. The fiber core boundary is indicated by the white circles.

Characteristics of spots formed by backpropagation of delta functions at different distances from the center of the core, for different sampling resolutions and using phase-only or amplitude-and-phase sampling: (a) longitudinal spot size, (b) transverse spot size, (c) centroid location, (d) peak sidelobe ratio and (e) integrated sidelobe ratio.